You'll have to get really, really good at reading the labels when you shop. Some snacks like kettle chips can be fried in peanut oil. Many, many baked goods or snacks are manufactured not using peanut ingredients but on the same equipment as peanut products. Plain M&Ms are one such snack.
Several types of nuts can be prepared in the same plant as other nuts.
Packages are required to list any allergy information, usually in bold just following the ingredient list. If a product is from the same machinery or the same facility with peanut products, the package will state this. One reason this is so important is that peanut particles become airborne and are easily spread around. They can sicken an allergic person just by their smell or proximity to the peanut product.
My 2-yr-old daughter is allergic to peanuts. We tested her for this because her father is highly allergic and has been to the emergency room on various occasions for this. We carry Epipens for both of them. Once I ate a Snickers at work, picked my DD up hours later and kissed her face. I won't make that mistake again - she broke out terribly all over and wheezed, but fortunately did not have a severe anaphylactic reaction that time. The reactions are known to get worse, not better, with repeated exposure in the case of a peanut allergy.
The most popular types of Thai dishes, like pad thai and Americanized dishes that go by names like "spicy Thai noodle" or "spicy Thai chicken wrap" will very frequently contain peanut sauce. We often order Thai food, but we always specify no peanuts on anything and tell them it's because of an allergy. Peanuts are often a garnish so it's easy to order without peanut, however we must be clear so that the chef will avoid cross-contamination. This may not be a risk you want to take, as well as dining inside a Thai restaurant where someone nearby may order a dish with peanuts. Sounds like your son is too young to let you know if he's bothered or sickened by the peanut aroma, so you may want to play it super safe on that.
I have found printable allergy cards available online, or those that you can purchase from www.achooallergy.com/foodallergycards.asp
These are intended to help communicate clearly with staff when eating out.
The main thing is to be super-vigilant. You never know what something contains, or the extent of awareness of people around you, including other parents, child care, food service workers.
Feel free to message me for any more info. I've been dealing with this since DD was small and fortunately have the insight of my boyfriend with the same allergy. Chick Fil A products cause him stomach cramps. You may read somewhere, as I did, that peanut oil is safe becuase it doesn't contain the protein, but don't risk it. He does have a mild reaction to just the oil.
I hope some of this helps,